Question

A balloon with mass ${}^{\prime }{m}^{\prime }$ is descending down with an acceleration ${}^{\prime }{a}^{\prime }$ (where $a<g$). How much mass should be removed from it so that it starts moving up with an acceleration ${}^{\prime }{a}^{\prime }$?

• A. $\frac{2ma}{g+a}$
• B. $\frac{2ma}{g-a}$
• C. $\frac{ma}{g+a}$
• D. $\frac{ma}{g-a}$

Answer 1

The correct option is A $\frac{2ma}{g+a}$

Let the upthrust of air be $F_b,$ then for downward motion
$mg-F_b=ma...\left(1\right)$
Let assume that mass $m^{\prime }$ be removed from the balloon
So, when it start moving upward
$F_b-(m-m^{\prime })g=(m-m^{\prime })a...\left(2\right)$

On adding equations $\left(1\right)\&\left(2\right)$
$mg-(m-m^{\prime })g=ma+(m-m^{\prime })a$
$m^{\prime }=\frac{2ma}{g+a}$